How does jem use stereotypes about gender to influence scout? how does scout feel about her gender? how do you know?

In Chapter 4 of In To Kill A Mockingbird by Harper Lee, Jem often uses the male superiority stereotype against Scout to make her feel guilty about anything he doesn't agree with her. For example, when Jem pushes Scout in the tire and it rolls onto the Radley's front yard, Jem tell her to go for tire. She refuses and Jem says "I swear, Scout, sometimes you act so much like a girl it's mortifyin'" As the story progress Scout starts doing things that men do so she would not be rejected from playing games.

"why don't you like me the way i am? " i cried. "i'm not a genius! i can't play the piano, and even if i could, i wouldn't go on tv if you paid me a million dollars! "

explanation:

the conflict between jing-mei and her mother is over jing-mei's piano lessons since her mother wants her to become a prodigy but she does not want to play it any more.